Species tree estimation from multiple markers is complicated by the fact that gene trees can differ from each other (and from the true species tree) due to several biological processes, one of which is gene duplication and loss. Local search heuristics for two NP-hard optimization problems - minimize gene duplications (MGD) and minimize gene duplications and losses (MGDL) - are popular techniqu...

In many scientific areas there is a frequent need to extract a common pattern from multiple data. In most cases, however, an approximate but low cost solution is preferred to a high cost exact match. To establish a fast search engine an efficient heuristic method should be implemented. Our investigation is devoted to the approximate nearest neighbor search (ANN) for unordered labeled trees. The...

The systematic investigation of countable universal graphs with “forbidden” subgraphs was initiated in [13], followed by [12]. If C is a finite connected graph, then a graph G is C-free if it contains no subgraph isomorphic to C. A countable C-free graph G is weakly universal if every countable C-free graph is isomorphic to a subgraph of G, and strongly universal if every such graph is isomorph...

The greedoid Tutte polynomial of a tree is equivalent to a generating function that encodes information about the number of subtrees with I internal (non-leaf) edges and L leaf edges, for all I and L. We prove that this information does not uniquely determine the tree T by constructing an infinite family of pairs of non-isomorphic caterpillars, each pair having identical subtree data. This disp...